Answer to Problem 57
To integrate

Equation 92
write

Equation 93

Equation 94
then

Equation 95

Equation 96
Integration with respect to
and
gives

Equation 97
Substitute
to get

Equation 98
Applying the boundary condition
, we find
:

Equation 99
Now use this equation to substitute for
in (*).

Equation 100

Equation 101
This gives

Equation 102
Let
. Then (6.4) simplifies to

Equation 103